Transfer Learning of Numerical Data
It seems like transfer learning is only applicable to neural networks. Is this a correct assumption?

No. Wiki page give you pointers of several examples in other methodologies.

While I was looking for examples of Transfer Learning, most seemed to be based on image data, audio data, or text data. I was not able to find an example of training a neural network on numerical data.

All the cases you say are converted to numerical data. Image and audio usually via sampling, text via one-hot encoding.

I want to use transfer learning in this particular scenario: I have a lot of numerical data from an old environment, with binary classification labels, and utilizing this, want to train on a new environment to do the same binary classification.

That is not transfer learning. Transfer learning applies when there are a change in the domain (input features) or in the task (output labels).

The dataset would look something like this Sample Table
Is this possible? What would the model look like?

For a simple case as the one you present, probably a simple network with one hidden layer will be enough. Train it with original pairs of {features,label} or, if not available, use the current predictor to obtain the label from the features.